Okay, so if god is allegorical for the immovable, unchanging is of the isness…
This sounds more like Aristotle’s Unmoved Mover than a religious god. The unfortunate problem for theists is they very quickly jump from such a vague analogy to a bizarre assortment of very specific irrational claims: favored denominations, being “born again”, being “saved by Jesus’ grace”, an obtusely judgmental “afterlife” that clearly devalues actual, real life, systems of morality that attempt to subvert the volitional nature of Man, etc.
But what’s the function of “an allegory for existence”? To conceptually clarify or confuse? I can construct an allegorical “infinite stack of turtles” to “represent existence”, but, so what? What good is it? To what in reality does it point?
…then how incompatible is it with Objectivism?
The most obvious answer is that Objectivism does not use allegories with defintionless terms as a substitute for actual metaphysical axioms.
When the burning bush says “i am the one true god, place no other god before me” is this not the theological equivalent to “a=a”?
Wood represents corruptible flesh (the “weakness” of man’s physical nature). Fire represents God & specifically his presence or judgment. The burning bush is God present in the form of a physical object that should be destroyed by the fire & yet “miraculously” is not. It is also a very important passage to Jews & Christians because this is where in their sacred text God forms a covenant with “his chosen people” through Moses.
So, this is a very heavily, religiously slanted “allegorical metaphor” from the outset.
Aside from all that nonsense, there is no such thing as “theological equivalence” to anything in Objectivist metaphysics.
If all religious truth follows from the word (creation) of the living god, and existence exists with reality being independent of mind, then where’s the dischord?
That is such a bad formulation it’s actual funny. 
It seems to me that Objectivists make two charges against religion: 1) that it is “mystical”, and 2) that it is altruistic.
He forgot the first one (& in my estimation the most important): religion is irrational. But I suppose that could be included in the mysticism charge.
If by labelling it “mystical” they imply that it defies reality, well, i’ll argue that religion is more allegorical than mystical and rather firmly asserts not only the independence of reality but it’s heirarchical supremacy.
This is evasion. At some point, every theist has to attempt to appeal to some irrational concept. At some point, every theological system attempt to assert that “something” exists to which they cannot point in reality.
Objectivists offer all kinds of explainations of emotions and feelings as subconcious calculations, but refuse to grant traditional knowledge via religion the same.
Objectivism explicitly states that emotions are not tools of cognition.
Objectvism is incomplete in the way that it refuses to explain the existence of faith.
I suppose you could make this claim if you’ve never read anything Ayn Rand wrote. You’d still be wrong, of course, but it would only be ignorance. Has this person read Atlas Shrugged, FTNI, PWNI?